Need help with Babylonians and Celts.

Babylon's bread and butter is either Lancers or Chariot Archers, depending on what advisors you chose. honourable mentions go to Royal Guards and Sappers

Celts are either Champions or Woad raiders with Druids along for healing and damage buff.

 

For a bit more detail, Babylon's Lancer spam can easily do most easy-mid lvl legendaries, and if your lancers are good you can do even the harder legendaries - The charge attack of the Lancers combined with being a fairly tanky cavalry unit makes them excellent at fighting infantry and range combinations, though if the enemy AI heavily uses anti-cav cavalry you'll want to mix in some mounted archers to help abate that. Keep in mind that Lancers aren't very good at taking out beefy buildings, so you'll want to keep a small contigent of either palitonins or Sappers depending on the map (Pals if you can, Sappers if the bonus objective is no pal/no siege. Generally 2-3 pals or 10-15 sappers are fine). You can use Neb to further buff Lancers, Chariot Rider Sargon to use the Chariot Archer or War Chariot builds, and finally General Zu enables the Royal Guard build, though keep in mind that Royal Guard's aren't great against heavy range.

For Celts, you actually have 4 different builds of varying viability - The most common is simple Woad Raider spam. Keep in mind that you'll want Brann the Bloodletter to make the most out of Woad builds. If you lack Brann, Champion+Druid is a solid build which doesn't require much to get rolling - Brennos is best, but the much cheaper Vercingtorix works as well. You'll want roughly 1 druid for every 3-4 champs in this combo. The 3rd build is Horseman+Carpetom via Commontorious - Horseman are used to tank and destroy buildings while Carpetoms kill everything. The final build is simple mass Bowman due to their high range, though it's also fairly gear dependent.

In terms of gear, if you go with Bowman/Chariot Archers, you'll want to maximize range for bow/arrow slot and damage(Crit on Bowman) on the armor slot. Lancers prefer build is Pharaoh's Spear of Destiny/Golden Hide of the Minotaur, though for the armor lesser armors with Bonus Damage Protection is good as well. Woad Raiders want to maximize damage on all 3 slots - Pure damage is best, don't listen to the goobers who say to max crit instead. Royal Guardsman want Apoc/Alexander's Breastplate as they already have a signifcant source of Bonus Damage protection from their advisor, either of the Vendor swords, and either Ares's War Shield or Shield of Rostam.
For Champions, the absolute BiS sword is Zahhak's Sword of the Undying due to Champion's high innate tankiness, though if you can't afford that the damage swords are solid. Due to the multiple HP buffs they can get, Delian Archon's Cuirass makes them the tankiest beating out Legion Enforcer's Breastplate that you use on other lesser medium armor units, but Apoc/Alex works too.
For Druids, you want maximum healing on their staff, and maximum health otherwise.
Horseman are geared the same as Lancers. For Carpetoms, you want Curse of the Archer along with damage cloth armor.

 

I main Celts, and frog.poison hit most of the beats I would have hit. I do personally use the event spears for both Lancers and Horsemen, and have been very happy with their performance.

Like they mentioned, Druids are pretty integral to a Champion build.

One thing I didn’t see them mention was Augar use; control-bind an Augar and keep them fed with Sacred Deer. Use their rites as often as you can, they have a substantial impact on your game, particularly in the Woad Raider build. That bonus damage vs. buildings can make or break a push sometimes.

 

While there isn't much time left...

The axe is best on Chieftain, as it basically allows the Chieftain to stay up forever as long as you don't have 20 archers focusing him. Keep in mind that unlike the other Zahhak weapons where it's a very minor damage loss, the Axe is a significant damage loss. I would not use it on Berserkers or Woads. Berserkers already have innate regen to help keep them healthy while traveling, and Woads are squish, all about getting that charge attack in then dying like extremely aggressive bees.
Axe could be useful on Harjar/Axemen if you plan on doing City Conquest/Defense as Egyptian/Norse often, as the health regen is actually strong on those maps.
Light Spear is EXTREMELY good on the Shield Bearer, Hoplite, Sparabara, and imo War Elephant - Especially the Shield Bearer, once you have them upgraded and they have the spear they can soak virtually all pierce damage forever and never, ever die. It's strong on the Sparabara since Sparabara are all about being frontline tanks, and Hoplites are also very tanky. As for War Elephants it helps to keep them topped off - One of the things I've noted about War Elephants is that either A) You run into heavy anti-cav cavalry, and all your Elephants die, or B) You don't run into that, and your Elephants slowly drop off one by one. Light Spear prevents the later scenario from happening, doing the Persian Legendaries and only having to replace a handful of Elephants throughout the push helps a lot.

Heavy Spear is great on the Cataphract, useful on the Lancer, but isn't the best for everything else. Though akin to how the Axe is good on Harjar/Axemen if you are doing City Conquest/Defense, the Heavy Spear is good in the same situation for Spearman and Horseman.

No comment on the Idol

 

For Berserker, you don't go completely full damage, no - Amun's Axe for weapon, Tunic of Actaeon for defense. As I see it on Berserker, you lose too much damage to justify the 8 HP/second regen especially when Berserker's already have innate regen.

And yea, for Sparabara's just make them tanky - Sparabara's have low damage, but they get absurd amounts of armor and health for how cheap and quick to make they are.

Though for Persia, once you hit the higher lvls, you'll tend to just mass Immortals, Cataphracts, Asabaras, or War Wagons instead. But if you decide to use Bowman for Persia, you'll want a mix of Sparabara for the frontline and Bowmen backing them up.

 

Zahhak's axe is good on berserkers. If you only have one piece, you can choose to move it to the chief and use an Amun's Axe of Ferocity on berserkers instead, but if you have 2 axes i'd definitely keep one on both units.

And yes, sparabara need to be tanky. They are a good frontline for priests, warwagons, archers etc.

 

As mentioned, the Light Spear is extremely good on the Shield Bearer - In fact, out of all the Zahhak weapons and units, the Shield Bearer actually gets the most benefit from Zahhak's. The regen from Zahhak's on a fully Pierce-Armor oriented Shield Bearer means that they need to take nearly 130 pierce damage per second in order to even start taking damage! Granted, they still die quickly to any other form of damage, but a single Shield Bearer with Zahhak's can tank multiple legendary guard towers, forts, or even archer bosses without a problem!